The present invention relates generally to adaptive controls, and more particularly to adaptive controls for uncertain nonlinear multi-input multi-output systems.
Aircraft autopilots have slow adaptive capabilities. To function in quickly changing environments, they resort to gain-scheduling of the controller parameters. A gain-scheduled autopilot is obtained by designing a set of controllers at different operating points and then linearly interpolating controller values between them. Extensive gain-scheduling may be a very expensive and time-consuming procedure. Traditional gain-scheduled autopilots react slowly to changes in conditions and can't compensate for significant changes in aircraft dynamics like sudden, unexpected, severe control surface failures or serious vehicle damage (e.g., having a wing sheared off).
The history of adaptive control is rich with methods for controlling systems in the presence of uncertainties. The development of these methods followed from the certainty equivalence principle. Assuming that the ideal parameters are known, conventional model reference adaptive control (MRAC) uses the nominal controller, parameterized in ideal parameters, to define the desired reference system based on perfect cancellation of uncertainties. Since the parameters are unknown, the adaptive controller is defined using the estimation of the unknown parameters from a gradient minimization scheme. Thus, one needs the estimation to be fast for better convergence, while on the other hand, increasing the speed of adaptation renders the adaptive controller high-gain and reduces the robustness of the closed-loop system to unmodeled dynamics, time-delays, etc. A common sense was that adaptive control is limited to slowly varying uncertainties, but the trade-off between the rate of variation of uncertainties and the performance was not quantified. Despite the stability guarantees, the practical implementation of adaptive controllers remained to be a challenge due to the lack of understanding how to tradeoff between adaptation, performance, and robustness. Because of these limitations, all successful implementations of adaptive controllers in use today are gain-scheduled, thus defeating the main point of adaptation.
Compared to the previous systems and methods of adaptive control, what is needed is an adaptive control that includes assured robustness in the presence of fast adaptation, thereby eliminating the need for gain-scheduling of the adaptive controller.